Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 1004)

Label	Polynomial	Discriminant	Galois group	Class group
20.16.1905147214615868315998879744.1	x^20 - 4x^19 - 10x^18 + 76x^17 - 76x^16 - 376x^15 + 1176x^14 - 488x^13 - 3416x^12 + 6654x^11 - 1826x^10 - 8228x^9 + 10419x^8 - 2880x^7 - 2526x^6 + 1562x^5 + 142x^4 - 204x^3 - 6x^2 + 10x + 1	\( 2^{30}\cdot 36497^{4} \)	20T669	Trivial (GRH)
20.16.2376038017203857413535432704.1	x^20 - 8x^19 + 14x^18 + 40x^17 - 135x^16 - 24x^15 + 282x^14 + 306x^13 - 543x^12 - 2060x^11 + 2840x^10 + 3536x^9 - 6398x^8 - 1810x^7 + 5674x^6 - 6x^5 - 1937x^4 + 124x^3 + 126x^2 - 22x + 1	\( 2^{30}\cdot 38569^{4} \)	20T669	Trivial (GRH)
20.16.2749111282333379101357955761.1	x^20 - 7x^19 + 4x^18 + 69x^17 - 125x^16 - 220x^15 + 658x^14 + 130x^13 - 1599x^12 + 745x^11 + 2341x^10 - 1813x^9 - 2567x^8 + 1464x^7 + 2013x^6 - 59x^5 - 561x^4 - 127x^3 + 29x^2 + 12x + 1	\( 17^{4}\cdot 67^{2}\cdot 157^{2}\cdot 4153^{4} \)	20T799	Trivial (GRH)
20.16.5969915757478328440239161344.1	x^20 - 2x^19 - 20x^18 + 44x^17 + 106x^16 - 234x^15 - 294x^14 + 638x^13 + 379x^12 - 1044x^11 + 10x^10 + 1102x^9 - 519x^8 - 814x^7 + 466x^6 + 410x^5 - 135x^4 - 110x^3 + 6x^2 + 10x + 1	\( 2^{30}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T86)	Trivial (GRH)
20.16.9297543283501805026208859136.1	x^20 - 8x^18 - 9x^16 + 140x^14 - 141x^12 - 297x^10 + 629x^8 - 432x^6 + 134x^4 - 19x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T751	Trivial (GRH)
20.16.10496183922101499053955078125.1	x^20 - 20x^18 - x^17 + 170x^16 + 21x^15 - 799x^14 - 180x^13 + 2258x^12 + 814x^11 - 3884x^10 - 2087x^9 + 3846x^8 + 3012x^7 - 1749x^6 - 2239x^5 - 74x^4 + 630x^3 + 251x^2 + 30x + 1	\( 5^{15}\cdot 61^{4}\cdot 397^{4} \)	20T369	Trivial (GRH)
20.16.17423096031535445218837890625.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 213x^16 + 276x^15 + 461x^14 - 1121x^13 - 307x^12 + 2011x^11 - 225x^10 - 2071x^9 + 453x^8 + 1359x^7 - 279x^6 - 562x^5 + 98x^4 + 120x^3 - 20x^2 - 8x + 1	\( 5^{10}\cdot 11^{2}\cdot 135049\cdot 10448989^{2} \)	20T1045	Trivial (GRH)
20.16.25465470084777436177937465344.1	x^20 - 20x^18 + 161x^16 - 667x^14 + 1515x^12 - 1892x^10 + 1315x^8 - 567x^6 + 175x^4 - 23x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 727^{2} \)	20T341	Trivial (GRH)
20.16.37430494635905898609287948941.1	x^20 - 10x^19 + 32x^18 - 3x^17 - 190x^16 + 296x^15 + 293x^14 - 1009x^13 + 141x^12 + 1429x^11 - 781x^10 - 963x^9 + 695x^8 + 315x^7 - 150x^6 - 81x^5 - 66x^4 + 28x^3 + 26x^2 - 3x - 1	\( 11^{16}\cdot 23^{2}\cdot 683^{2}\cdot 3301 \)	20T846	Trivial (GRH)
20.16.40942957151311819052087771136.1	x^20 - 22x^18 + 191x^16 - 836x^14 + 1927x^12 - 2068x^10 + 251x^8 + 1126x^6 - 342x^4 - 228x^2 + 1	\( 2^{30}\cdot 3^{10}\cdot 71^{8} \)	20T538	Trivial (GRH)
20.16.47752675419906880734391798001.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 115x^16 + 308x^15 - 111x^14 - 533x^13 + 764x^12 + 5x^11 - 902x^10 + 731x^9 + 199x^8 - 623x^7 + 266x^6 + 134x^5 - 158x^4 + 28x^3 + 20x^2 - 9x + 1	\( 607^{2}\cdot 37649^{2}\cdot 41579^{2}\cdot 52889 \)	20T1110	Trivial (GRH)
20.16.49163069859207319641806640625.1	x^20 - x^19 - 19x^18 + 30x^17 + 98x^16 - 232x^15 - 135x^14 + 834x^13 - 121x^12 - 1724x^11 + 117x^10 + 1990x^9 + 583x^8 - 1038x^7 - 702x^6 + 210x^5 + 271x^4 - 18x^3 - 39x^2 + 3x + 1	\( 5^{10}\cdot 11^{16}\cdot 331^{2} \)	$C_2^2\times C_2^4:C_5$ (as 20T86)	Trivial (GRH)
20.16.78373863200973734627971716729.1	x^20 - 2x^19 - 17x^18 + 30x^17 + 84x^16 - 196x^15 + 49x^14 + 931x^13 - 1429x^12 - 3194x^11 + 3803x^10 + 6374x^9 - 3734x^8 - 6819x^7 + 689x^6 + 3565x^5 + 984x^4 - 621x^3 - 429x^2 - 69x - 1	\( 3^{6}\cdot 401^{10} \)	$C_2\times C_2^4:D_5$ (as 20T81)	Trivial (GRH)
20.16.85328038161196365058360047409.1	x^20 - 5x^19 - 4x^18 + 44x^17 - 5x^16 - 118x^15 - 24x^14 - 33x^13 + 421x^12 + 821x^11 - 1266x^10 - 1964x^9 + 1566x^8 + 2387x^7 - 842x^6 - 1631x^5 + 167x^4 + 572x^3 - 14x^2 - 73x + 1	\( 11^{18}\cdot 43^{4}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.16.87806017036757415782119140625.1	x^20 - x^19 - 13x^18 + 8x^17 + 25x^16 + 54x^15 + 105x^14 - 371x^13 - 364x^12 + 740x^11 + 260x^10 - 564x^9 + 186x^8 + 43x^7 - 289x^6 + 130x^5 + 104x^4 - 44x^3 - 16x^2 + 4x + 1	\( 5^{10}\cdot 111847^{2}\cdot 847789^{2} \)	20T1021	Trivial (GRH)
20.16.96099805831627363000043700224.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 167x^16 + 316x^15 + 122x^14 - 876x^13 + 545x^12 + 838x^11 - 1187x^10 - 22x^9 + 876x^8 - 440x^7 - 208x^6 + 248x^5 - 30x^4 - 44x^3 + 15x^2 + 2x - 1	\( 2^{20}\cdot 9649^{2}\cdot 93629^{2}\cdot 112289 \)	20T1110	Trivial (GRH)
20.16.97738885512935359526308151296.1	x^20 - 8x^19 + 18x^18 + 12x^17 - 150x^16 + 422x^15 - 434x^14 - 960x^13 + 3223x^12 - 1716x^11 - 4955x^10 + 6682x^9 + 2165x^8 - 6870x^7 + 322x^6 + 3148x^5 - 310x^4 - 640x^3 + 19x^2 + 34x - 1	\( 2^{40}\cdot 31^{4}\cdot 557^{4} \)	20T368	Trivial (GRH)
20.16.106728174141502165470995808256.1	x^20 - 20x^18 - 10x^17 + 112x^16 + 180x^15 - 422x^14 - 838x^13 + 1344x^12 + 1554x^11 - 2714x^10 - 1228x^9 + 2945x^8 + 252x^7 - 1610x^6 + 156x^5 + 396x^4 - 70x^3 - 32x^2 + 4x + 1	\( 2^{30}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T799	Trivial (GRH)
20.16.118633445252727603200000000000.1	x^20 - 6x^19 - 2x^18 + 68x^17 - 53x^16 - 288x^15 + 114x^14 + 1288x^13 - 356x^12 - 4480x^11 + 4204x^10 + 3960x^9 - 6770x^8 + 584x^7 + 3098x^6 - 980x^5 - 577x^4 + 170x^3 + 50x^2 - 4x - 1	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.16.118633445252727603200000000000.2	x^20 - 2x^19 - 17x^18 + 28x^17 + 93x^16 - 174x^15 - 178x^14 + 568x^13 - 81x^12 - 854x^11 + 945x^10 + 192x^9 - 2093x^8 + 642x^7 + 2336x^6 - 332x^5 - 1113x^4 - 4x^3 + 185x^2 + 14x - 1	\( 2^{24}\cdot 5^{11}\cdot 3469^{4} \)	20T755	Trivial (GRH)
20.16.154181708612560135336755200000.1	x^20 - 6x^19 - 8x^18 + 124x^17 - 201x^16 - 544x^15 + 2204x^14 - 1782x^13 - 3551x^12 + 8740x^11 - 5372x^10 - 3014x^9 + 5340x^8 - 2100x^7 + 654x^6 - 952x^5 + 505x^4 + 6x^3 - 46x^2 + 2x + 1	\( 2^{30}\cdot 5^{5}\cdot 11^{16} \)	20T427	Trivial (GRH)
20.16.190320820825165748285615374336.1	x^20 - 9x^18 + x^16 + 278x^14 - 1410x^12 + 3254x^10 - 3925x^8 + 2351x^6 - 534x^4 - 9x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T673	Trivial (GRH)
20.16.190320820825165748285615374336.2	x^20 - 15x^18 + 80x^16 - 149x^14 - 154x^12 + 959x^10 - 1040x^8 - 205x^6 + 764x^4 - 181x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T673	Trivial (GRH)
20.16.190320820825165748285615374336.3	x^20 - 15x^18 + 82x^16 - 203x^14 + 190x^12 + 101x^10 - 310x^8 + 127x^6 + 72x^4 - 45x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.16.190320820825165748285615374336.4	x^20 - 5x^18 - 10x^16 + 83x^14 - 71x^12 - 242x^10 + 544x^8 - 426x^6 + 147x^4 - 21x^2 + 1	\( 2^{32}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.16.200540506089835653323720703125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 145x^16 + 344x^15 - 72x^14 - 722x^13 + 987x^12 + 110x^11 - 1459x^10 + 1052x^9 + 682x^8 - 1142x^7 + 98x^6 + 446x^5 - 160x^4 - 57x^3 + 34x^2 - 1	\( 5^{10}\cdot 11^{16}\cdot 446909 \)	20T409	Trivial (GRH)
20.16.206548481879697235603429344256.1	x^20 - 9x^18 + 9x^16 + 122x^14 - 437x^12 + 515x^10 - 80x^8 - 271x^6 + 182x^4 - 34x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.16.206548481879697235603429344256.2	x^20 - 14x^18 + 68x^16 - 115x^14 - 75x^12 + 464x^10 - 466x^8 + 80x^6 + 66x^4 - 21x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.16.206548481879697235603429344256.3	x^20 - x^18 - 52x^16 + 204x^14 - 219x^12 - 125x^10 + 439x^8 - 362x^6 + 135x^4 - 22x^2 + 1	\( 2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T676	Trivial (GRH)
20.16.206667906113530203898777698304.1	x^20 - 10x^18 + 25x^16 + 39x^14 - 256x^12 + 339x^10 - 48x^8 - 167x^6 + 94x^4 - 17x^2 + 1	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 757^{2} \)	20T994	Trivial (GRH)
20.16.206667906113530203898777698304.2	x^20 - 8x^18 + 15x^16 + 33x^14 - 149x^12 + 153x^10 + 24x^8 - 122x^6 + 67x^4 - 14x^2 + 1	\( 2^{20}\cdot 61^{4}\cdot 397^{4}\cdot 757^{2} \)	20T994	Trivial (GRH)
20.16.239979839737589598767078703104.1	x^20 - 2x^19 - 26x^18 + 52x^17 + 223x^16 - 538x^15 - 624x^14 + 2632x^13 - 1025x^12 - 5288x^11 + 7940x^10 - 328x^9 - 8746x^8 + 9440x^7 - 5322x^6 + 2014x^5 - 279x^4 - 236x^3 + 136x^2 - 24x + 1	\( 2^{30}\cdot 101\cdot 38569^{4} \)	20T992	Trivial (GRH)
20.16.276046894426236664438661840896.1	x^20 - 16x^18 + 106x^16 - 375x^14 + 759x^12 - 864x^10 + 482x^8 - 53x^6 - 52x^4 + 12x^2 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.16.276046894426236664438661840896.2	x^20 - 14x^18 + 79x^16 - 225x^14 + 318x^12 - 135x^10 - 166x^8 + 182x^6 - 16x^4 - 24x^2 + 1	\( 2^{20}\cdot 460181^{2}\cdot 1114969^{2} \)	20T1105	Trivial (GRH)
20.16.283852656623852252960205078125.1	x^20 - 15x^18 + 75x^16 - 120x^14 - 105x^12 + 475x^10 - 360x^8 - 50x^6 + 145x^4 - 50x^2 + 5	\( 5^{23}\cdot 47^{8} \)	20T135	Trivial (GRH)
20.16.303899715661508400040000000000.1	x^20 - 7x^18 - 32x^16 + 347x^14 - 513x^12 - 2288x^10 + 8671x^8 - 10537x^6 + 4896x^4 - 715x^2 + 1	\( 2^{12}\cdot 5^{10}\cdot 52501^{4} \)	20T638	Trivial (GRH)
20.16.303899715661508400040000000000.2	x^20 - 15x^18 + 86x^16 - 225x^14 + 206x^12 + 202x^10 - 529x^8 + 286x^6 + x^4 - 18x^2 + 1	\( 2^{12}\cdot 5^{10}\cdot 52501^{4} \)	20T760	Trivial (GRH)
20.16.344255425354822086003595935744.1	x^20 - 13x^18 + 59x^16 - 96x^14 - 39x^12 + 287x^10 - 310x^8 + 125x^6 - 8x^4 - 6x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.16.344255425354822086003595935744.2	x^20 - 13x^18 + 48x^16 + 3x^14 - 314x^12 + 430x^10 + 64x^8 - 238x^6 + 102x^4 - 17x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.16.344255425354822086003595935744.3	x^20 - 9x^18 + 15x^16 + 74x^14 - 259x^12 + 43x^10 + 724x^8 - 961x^6 + 410x^4 - 38x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.344255425354822086003595935744.4	x^20 - 7x^18 - 6x^16 + 119x^14 - 195x^12 - 131x^10 + 499x^8 - 391x^6 + 130x^4 - 19x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.344255425354822086003595935744.5	x^20 - 9x^18 + 15x^16 + 63x^14 - 215x^12 + 142x^10 + 141x^8 - 213x^6 + 91x^4 - 16x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.344255425354822086003595935744.6	x^20 - 17x^18 + 113x^16 - 370x^14 + 581x^12 - 197x^10 - 666x^8 + 949x^6 - 458x^4 + 64x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.16.361584833516665893892275390625.1	x^20 - 4x^19 - 13x^18 + 64x^17 + 48x^16 - 388x^15 - 84x^14 + 1291x^13 + 374x^12 - 2319x^11 - 1147x^10 + 2195x^9 + 1545x^8 - 1018x^7 - 958x^6 + 181x^5 + 262x^4 - x^3 - 28x^2 - x + 1	\( 5^{10}\cdot 1483^{2}\cdot 129751961^{2} \)	20T1021	Trivial (GRH)
20.16.379627024808728330240000000000.1	x^20 - 16x^18 + 92x^16 - 176x^14 - 364x^12 + 2312x^10 - 4144x^8 + 3024x^6 - 528x^4 - 176x^2 + 16	\( 2^{28}\cdot 5^{10}\cdot 3469^{4} \)	20T760	Trivial (GRH)
20.16.403039616093946308416220703125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 142x^16 + 320x^15 - 12x^14 - 722x^13 + 765x^12 + 350x^11 - 1243x^10 + 632x^9 + 613x^8 - 854x^7 + 155x^6 + 323x^5 - 218x^4 - 4x^3 + 46x^2 - 13x + 1	\( 5^{10}\cdot 11^{2}\cdot 430061\cdot 28162171^{2} \)	20T1045	Trivial (GRH)
20.16.437402377341742634765604880384.1	x^20 - 12x^18 + 54x^16 - 105x^14 + 50x^12 + 110x^10 - 146x^8 + 37x^6 + 18x^4 - 9x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2}\cdot 131^{2} \)	20T751	Trivial (GRH)
20.16.443120666588748018536869265408.1	x^20 - 19x^18 + 158x^16 - 755x^14 + 2282x^12 - 4514x^10 + 5832x^8 - 4757x^6 + 2270x^4 - 544x^2 + 47	\( 2^{20}\cdot 47\cdot 111847^{2}\cdot 847789^{2} \)	20T1110	Trivial (GRH)
20.16.502594097946671319040000000000.1	x^20 - 19x^18 + 160x^16 - 781x^14 + 2421x^12 - 4908x^10 + 6472x^8 - 5367x^6 + 2615x^4 - 656x^2 + 61	\( 2^{20}\cdot 5^{10}\cdot 61\cdot 3169^{2}\cdot 8951^{2} \)	20T1045	Trivial (GRH)
20.16.510934781922934055328369140625.1	x^20 - 5x^19 - 15x^18 + 100x^17 + 40x^16 - 706x^15 + 355x^14 + 2075x^13 - 2440x^12 - 2235x^11 + 5922x^10 + 1335x^9 - 6420x^8 - 6465x^7 + 140x^6 + 9461x^5 + 6090x^4 - 1005x^3 - 835x^2 + 130x - 4	\( 3^{2}\cdot 5^{22}\cdot 47^{8} \)	20T140	Trivial (GRH)